The characterization of Gaussian operations and Distillation of Gaussian States
arXiv:quant-ph/0204085 · doi:10.1103/PhysRevA.66.032316
Abstract
We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations which can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes which can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.
8 pages, revtex4; v4: published version; v3: more details on V(gamma), some typos corrected, formulations clarified
References in corpus (9)
- A computable measure of entanglement
- Continuous variable quantum cryptography using coherent states
- Generation of Continuous Variable Einstein-Podolsky-Rosen Entanglement via the Kerr Nonlinearity in an Optical Fibre
- Separability Criterion for all bipartite Gaussian States
- Distillability Criterion for all Bipartite Gaussian States
- Quantum key distribution with bright entangled beams
- Improving fidelity of continuous-variable teleportation via local operations
- Generalized coherent states
- Conditions for the local manipulation of Gaussian states
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